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Rado's theorem for polymatroids

Published online by Cambridge University Press:  24 October 2008

Colin J. H. McDiarmid
Colin J. H. McDiarmid
Affiliation:
Corpus Christi College, Oxford
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Extract

The theorem of R. Rado (12) to which I refer by the name ‘Rado's theorem for matroids’ gives necessary and sufficient conditions for a family of subsets of a finite set Y to have a transversal independent in a given matroid on Y. This theorem is of fundamental importance in both transversal theory and matroid theory (see, for example, (11)). In (3) J. Edmonds introduced and studied ‘polymatroids’ as a sort of continuous analogue of a matroid. I start this paper with a brief introduction to polymatroids, emphasizing the role of the ‘ground-set rank function’. The main result is an analogue for polymatroids of Rado's theorem for matroids, which I call not unnaturally ‘Rado's theorem for polymatroids’.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 78 , Issue 2 , September 1975 , pp. 263 - 281
Copyright
Copyright © Cambridge Philosophical Society 1975

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References

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